Arithmetic Sequences

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

Front

How do you find the common difference in an arithmetic sequence?

Back

The common difference (d) can be found by subtracting any term from the subsequent term: d = a(n+1) - a(n).

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term (a_n) can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

Find the next three terms in the arithmetic sequence: 9, 19, 29, 39, ...

Back

49, 59, 69

Front

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

Back

3, 12, 21

Front

Find the 22nd term of the following sequence: 5, 8, 11, ...

Back

68

Front

Find a_26 in the arithmetic sequence: -15, -35, -55, -75, ...

Back

-515

Front

Find the next three terms in the arithmetic sequence: -3, -8, -13, -18, ...

Back

-23, -28, -33

Front

What is the first term of an arithmetic sequence?

Back

The first term (a_1) is the initial term of the sequence from which all other terms are derived.

Front

What does it mean if the common difference is negative in an arithmetic sequence?

Back

If the common difference is negative, the terms of the sequence decrease as you move from one term to the next.